Deflation and polynomial preconditioning in the application of the overlap operator at nonzero chemical potential

When solving linear systems with the overlap operator at nonzero chemical potential $\mu$ in lattice QCD one needs, at every iteration of the iterative solver, to apply the sign function evaluated on a non-Hermitian operator $Q_{\mu}$ times a vector, i.e., $\mathrm{sign}(Q_{\mu})v$. In this work we describe how deflation and (the more recently proposed) polynomial preconditioning can be applied to this problem, in particular in the context of lattice QCD. Furthermore, we describe how both methods can be combined, we compare them in numerical experiments and explore whether there might be any synergy between both that can be exploited.